

lowercase			:				Dict   =     [sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(10_00_00)]






def        snake_case__		(    lowerCamelCase_		):
							A      :					List[str]      		=					0
							while number:
														# Increased Speed Slightly by checking every 5 digits together.
														sum_of_digits_squared += DIGITS_SQUARED[number % 100000]
														number //= 100000

							return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
lowercase			:				list[bool | None]   =     [None] * 10_00_00_00
lowercase			:				int   =     True
lowercase			:				Tuple   =     False






def        snake_case__		(    lowerCamelCase_		):

							if CHAINS[number - 1] is not None:
														return CHAINS[number - 1]  # type: ignore

							A      :					int      		=					chain(next_number(lowerCamelCase_		)		)
							A      :					Dict      		=					number_chain

							while number < 10000000:
														A      :					Any      		=					number_chain
														number *= 10

							return number_chain






def        snake_case__		(    lowerCamelCase_ = 10000000		):
							for i in range(1     ,				lowerCamelCase_		):
														if CHAINS[i] is None:
																					chain(i + 1		)

							return CHAINS[:number].count(lowerCamelCase_		)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(F"{solution() = }")









import inspect
from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel, VQModel
from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class 					__lowercase  (						_SCREAMING_SNAKE_CASE				):





							"""simple docstring"""

							def __init__(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       Any:
														super().__init__()
														self.register_modules(vqvae=__UpperCAmelCase    ,						unet=__UpperCAmelCase    ,						scheduler=__UpperCAmelCase						)






							@torch.no_grad()
							def __call__(					self    ,						__UpperCAmelCase = 1    ,						__UpperCAmelCase = None    ,						__UpperCAmelCase = 0.0    ,						__UpperCAmelCase = 50    ,						__UpperCAmelCase = "pil"    ,						__UpperCAmelCase = True    ,						**__UpperCAmelCase    ,						)		->       Union[Tuple, ImagePipelineOutput]:
														A      :					List[Any]      		=					randn_tensor(
														    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)    ,						generator=__UpperCAmelCase    ,						)
														A      :					List[Any]      		=					latents.to(self.device						)

														# scale the initial noise by the standard deviation required by the scheduler
														A      :					Optional[int]      		=					latents * self.scheduler.init_noise_sigma

														self.scheduler.set_timesteps(__UpperCAmelCase						)

														# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
														A      :					str      		=					'''eta''' in set(inspect.signature(self.scheduler.step						).parameters.keys()						)

														A      :					List[str]      		=					{}
														if accepts_eta:
																					A      :					Optional[Any]      		=					eta

														for t in self.progress_bar(self.scheduler.timesteps						):
																					A      :					Any      		=					self.scheduler.scale_model_input(__UpperCAmelCase    ,						__UpperCAmelCase						)
																					# predict the noise residual
																					A      :					Dict      		=					self.unet(__UpperCAmelCase    ,						__UpperCAmelCase						).sample
																					# compute the previous noisy sample x_t -> x_t-1
																					A      :					int      		=					self.scheduler.step(__UpperCAmelCase    ,						__UpperCAmelCase    ,						__UpperCAmelCase    ,						**__UpperCAmelCase						).prev_sample

														# decode the image latents with the VAE
														A      :					str      		=					self.vqvae.decode(__UpperCAmelCase						).sample

														A      :					Tuple      		=					(image / 2 + 0.5).clamp(0    ,						1						)
														A      :					int      		=					image.cpu().permute(0    ,						2    ,						3    ,						1						).numpy()
														if output_type == "pil":
																					A      :					Union[str, Any]      		=					self.numpy_to_pil(__UpperCAmelCase						)

														if not return_dict:
																					return (image,)

														return ImagePipelineOutput(images=__UpperCAmelCase						)






